Portable battery powered devices, such as mobile telephones, Personal Digital Assistants, MP3 players, and the like, need to be low cost, low powered, and compact. Therefore, many such devices utilize switching power supplies to minimize space and power consumption. Switching power supplies use inductors as energy storage and filtering elements, and since many electronic devices use a printed circuit board (PCB) framework in their construction, PCB based inductors, which are also called PCB inductors, are often used in switching power supplies.
A PCB is a flat, laminated board with at least one layer of insulating material, and at least one layer of conducting material. Multilayer PCBs include alternating layers of insulating materials and conducting materials. Electrical circuits are formed by either etching away conducting materials, or adding conducting materials by plating or deposition. Typical conducting materials include copper, tin, lead, gold, and silver. Typical insulating materials include glass epoxies and resin-based preimpregnated materials (prepreg).
A PCB inductor is typically formed using a spiral pattern on at least one PCB conducting layer. The magnetic field of the inductor follows a magnetic path, which is orthogonal to the conduction path. The inductance is limited by the effective number of turns that can be formed, and the effective magnetic permeability of the magnetic path. One type of PCB inductor is shown in U.S. Pat. No. 6,996,892.
FIG. 1 shows the construction of a traditional inductor. A winding 10 is wrapped around a magnetic core 12. The number of times the winding is wrapped around the core is known as the number of turns N of the inductor. The magnetic core 12 may form a contiguous magnetic path, or a magnetic path with an air gap 14. The inductance L of the inductor is dependent upon N and the total reluctance ST Of the magnetic path, which is the sum of the core reluctance SC and the air gap reluctance SA. L is equal to the product of N and the total flux φ in the inductor divided by the inductor current i. Magneto-motive force MMF is the driving force in a magnetic circuit, and is equal to the product of N and the inductor current i. Magnetic reluctance, also called reluctance S, is equal to magneto-motive force MMF divided by the total flux φ, which is developed in response to the MMF. For a uniform magnetic circuit, reluctance S is equal to the length I of the magnetic circuit divided by the product of the cross-sectional area A, the magnetic permeability of free space u0, and the relative magnetic permeability ur of the material forming the magnetic circuit. The following equations illustrate the dependencies of inductance L on the reluctances of the core and air gap SC, SA.S=MMF/φ=Ni/φor φ=Ni/S  EQ. 1S=I/u0urA  EQ. 2For the core—SC=IC/u0urAC  EQ. 3For the air gap—SA=IA/u0AA  EQ. 4L=Nφ/i  EQ. 5Now substituting EQ. 1 into EQ. 5:L=N(Ni/S)/i=N2/S=N2/ST=N2/(SA+SC)From EQ. 6, the inductance L is inversely proportional to the total reluctance ST; therefore, the inductance can be increased by minimizing the total reluctance ST, which is the sum of SA and SC. The relationship of SA and SC can be analyzed by examining the ratio of SA to SC as shown below:SA/SC=(IA/u0AA)/(IC/u0urAC)  EQ. 7If the cross-sectional areas of the core and the gap are equal, then EQ. 7 reduces to:SA/SC=ur(IA/IC)  EQ. 8From EQ. 8, if the relative magnetic permeability ur of the core material is 1000, which is not unusual, then even if the air gap length IA is only 1% of the core length IC, the reluctance of the air gap SA is ten times greater than the reluctance of the core SC. Therefore, the inductance is mainly determined by reluctance of the air gap SA and the number of turns N.
Since PCB inductors utilize insulating layers, which typically have low magnetic permeability, similar to that of air gaps, in their magnetic path, large inductance PCB inductors are not practical in many applications. Some PCB inductors use conductive layers of magnetic materials to help reduce total reluctance; however, cross-sectional areas are limited since the thicknesses of conductor layers are relatively thin and insulating layers are not eliminated. From the analysis in the previous paragraph, if low magnetic permeability gaps can be minimized or eliminated, PCB inductors with higher inductances can be constructed.